Abstract
Recently new operations have been defined for soft sets. In this paper, we study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. Finally, we show that soft sets with a fixed set of parameters are MV algebras and BCK algebras.
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